Solve the Expression: (xy+2a)(x-2b) Binomial Multiplication

Q: Why does xy times x equal x²y and not x²?

When multiplying xy × x, you multiply all parts: x × x = x² and y stays as y, giving you x²y. Think of it as (x)(y) × (x) = (x²)(y).

Q: How do I keep track of all the signs?

Write each multiplication step clearly: xy × (-2b) = -2xyb. The negative sign from -2b carries through to make the term negative.

Q: Can I rearrange the terms in my final answer?

Yes! $ x^2y - 2xyb + 2ax - 4ab $ could also be written as $ x^2y + 2ax - 2xyb - 4ab $. The order doesn't matter in addition.

Q: What if I get confused with so many variables?

Take it one step at a time! Write out each FOIL step separately before combining. It's better to be slow and accurate than fast and wrong.

Binomial Multiplication with Multivariable Terms

Solve the exercise:

$(xy+2a)\cdot(x-2b)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Open parentheses properly, multiply each factor by each factor

00:26 Let's calculate the multiplications

00:54 Positive times negative always equals negative

01:03 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the exercise:

$(xy+2a)\cdot(x-2b)=$

Step-by-step solution

To solve the problem $(xy + 2a) \cdot (x - 2b)$ , we will use the distributive property, commonly referred to as the FOIL method for binomials. This involves multiplying each term in the first binomial by each term in the second binomial:

First: Multiply the first terms of each binomial: $xy \times x = x^2y$ .
Outside: Multiply the outer terms: $xy \times (-2b) = -2xyb$ .
Inside: Multiply the inner terms: $2a \times x = 2ax$ .
Last: Multiply the last terms: $2a \times (-2b) = -4ab$ .

Next, we combine these four results to form the expanded expression:

$x^2y - 2xyb + 2ax - 4ab$

Thus, the correct expression after using the distributive property and simplifying is $x^2y - 2xyb + 2ax - 4ab$ .

Final Answer

_{^{$x^2y-2xyb+2ax-4ab$}}

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outside, Inside, Last multiplication steps
Technique: xy × x = x²y, keep variables together
Check: Count terms: should have 4 terms after expanding ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply variables correctly
Don't just multiply coefficients and ignore variables = missing variable terms! When multiplying xy × x, the result is x²y, not just xy. Always multiply all parts of each term including variables and their exponents.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

Why does xy times x equal x²y and not x²?

When multiplying xy × x, you multiply all parts: x × x = x² and y stays as y, giving you x²y. Think of it as (x)(y) × (x) = (x²)(y).

How do I keep track of all the signs?

Write each multiplication step clearly: xy × (-2b) = -2xyb. The negative sign from -2b carries through to make the term negative.

Can I rearrange the terms in my final answer?

Yes! $x^2y - 2xyb + 2ax - 4ab$ could also be written as $x^2y + 2ax - 2xyb - 4ab$ . The order doesn't matter in addition.

What if I get confused with so many variables?

Take it one step at a time! Write out each FOIL step separately before combining. It's better to be slow and accurate than fast and wrong.

How do I know I expanded correctly?

Count your terms! A binomial times a binomial should give you 4 terms before combining like terms. If you have fewer, you missed a multiplication.

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